Modelling and Control of HIV/AIDS Propagation - A Case Study of the Ashanti Region of Ghana

Abstract

HIV/AIDS constitutes a grave threat to the socio-economic development of all nations but especially those in the sub-Sahara Africa. This study has been carried out to model the population, age and gender structure dynamics of the reported cases of HIV/AIDS in the Ashanti Region of Ghana for the period 1982 to 2001 with a view to assessing the level and impact of the pandemic as well as the effectiveness of the existing control measures. A statistical method of system identification based on vector autoregressive time series analysis was used. This led in most cases to deterministic discrete – time linear autonomous models. The population dynamics of reported HIV/AIDS cases for females and males were found to be of second order, unstable, growing linearly in the mean but with a sinusoidal oscillation of period 4.2 years. Three age groups with common dynamical characteristics were identified: the 0 – 19, the 20 – 49 and the 50+ year age groups. Each of these age groups, however, had first order dynamics, which were stable reaching equilibrium levels in a few decades. Further analysis involving the computation of the controllability matrix revealed that condom utilization as a method of controlling HIV/AIDS has no significant impact in the control of the number of
reported cases.

Journal of the Ghana Science Association Vol. 9 (2) 2007: pp. 94-104